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The first of two volumes on anabelian algebraic geometry, this book contains the famous manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. This work, written fourteen years after his retirement from public life in mathematics, includes the closely related letter to Gerd Faltings, published for the first time in this volume. Together these documents describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves. The book is written in an artistic and informal style. It contains several articles on subjects directly related to the ideas explored in the manuscripts, including surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.
1. Esquisse d'un programme A. Grothendieck; 2. Letter to Faltings A. Grothendieck; 3. The Algebraic fundamental group F. Oort; 4. Grothendieck's 'Long March through Galois Theory' L. Schneps; 5. Survey of the anabelian conjecture F. Pop; 6. Etale homotopy type of the moduli spaces of algebraic curves T. Oda; 7. Tame topology B. Teissier; 8. The obvious part of Belyi's theorem and Riemann surfaces with many automorphisms J. Wolfart; 9. Singularities of moduli spaces, Galois cartography and finite projective geometry V. Adrianov and G. Shabat; 10. π1 of moduli spaces at infinity P. Lochak; 11. Galois actions on higher genus mapping class groups H. Nakamura; 12. On GT L. Schneps; 13. On the GT action on covers D. Harbater and L. Schneps; 14. Two letters on non-abelian cohomology J.-P. Serre.